The polynomial p(t)=t3−3t2+2t−4p(t) = t^3 - 3t^2 + 2t - 4p(t)=t3−3t2+2t−4 has the companion matrix C=[00410−2013]C = \begin{bmatrix} 0 & 0 & 4 \\ 1 & 0 & -2 \\ 0 & 1 & 3 \end{bmatrix}C=0100014−23. Which statements are true?
The characteristic polynomial of CCC is det(λI−C)=p(λ)\det(\lambda I - C) = p(\lambda)det(λI−C)=p(λ)
The eigenvalues of CCC are the roots of p(t)p(t)p(t)
The minimal polynomial of CCC always equals p(λ)p(\lambda)p(λ) regardless of root multiplicities
The matrix CCC is always diagonalizable